INPUTS

number of requests in the system (scalar, N > 0).

D(k)

service demand of service center $k$ (D(k) ≥ 0).

S(k)

mean service time at center $k$ (S(k) ≥ 0).

V(k)

visit ratio to center $k$ (V(k) ≥ 0).

m(k)

number of servers at center $k$. This function only supports $M/M/1$ queues, therefore m must be ones(size(S)).

Z

external delay (think time, Z ≥ 0). Default 0.

OUTPUTS

Xl

Xu

Lower and upper bounds on the system throughput.

Rl

Ru

Lower and upper bounds on the system response time.

REFERENCES

• C. H. Hsieh and S. Lam, Two classes of performance bounds for closed queueing networks, Performance Evaluation, Vol. 7 Issue 1, pp. 3–30, February 1987, DOI 10.1016/0166-5316(87)90054-X. Also available as Technical Report TR-85-09, Department of Computer Science, University of Texas at Austin, June 1985

This function implements the non-iterative variant described in G. Casale, R. R. Muntz, G. Serazzi, Geometric Bounds: a Non-Iterative Analysis Technique for Closed Queueing Networks, IEEE Transactions on Computers, 57(6):780-794, June 2008.

See also: qncsaba, qbcsbsb, qncsgb